Preheat oven to 350 degrees. Line large baking sheets with parchment paper.

In the bowl of an electric mixer, butter, oil, granulated sugar, powdered sugar, vanilla, eggs, and pumpkin puree. Continue beating at medium-high speed until very light and fluffy, 4-5 minutes. 

Mix in baking soda, cream of tartar, salt, pumpkin pie spice. Gradually add flour, mixing until well combined.

Form the dough into 1/4 cup sized balls. Roll the balls in sugar to coat. Placed on prepared baking sheets. Use the bottom of a tall glass or cup to flatten the cookie to about 1/2 inch thickness. The sides of the dough should squish out around the bottom of the glass to form an edge. Repeat with remaining dough, placing 6-8 cookies per baking sheet.

Bake for about 10 minutes, or until cookies are just set and beginning to turn golden. Let cookies rest for a few minutes on the baking sheet before transferring to a wire rack to cook completely.

To make the frosting: Beat the butter, sour cream, vanilla, powdered sugar, salt and pumpkin pie spice until well mixed. Add additional powdered sugar, if desired, for a thicker frosting. Spread frosting over cooled cookies.